Brendan Rodgers said Liverpool's 4-0 destruction of Everton would have a major psychological impact on the race for Champions League qualification as Daniel Sturridge delivered two goals plus an apology at Anfield.

Sturridge struck twice in barely two minutes to add to Steven Gerrard's headed opener before Luis Suárez sealed an emphatic Merseyside derby win for Liverpool over one of their rivals for a top-four place. The England striker also missed the chance to compound Everton's embarrassment from the penalty spot, and to set up Suárez for a fifth goal, before being substituted and exchanging words with the Liverpool manager as he left the pitch.

Rodgers insisted Sturridge's withdrawal was for tactical reasons and that the player had not shown disrespect with his annoyed response. But the striker said: "I apologise for my reaction. I was disappointed by missing the penalty and felt I'd let myself down as well as the fans. The hat-trick would have been the icing on the cake and it's unfortunate. I was disappointed with myself. It was nothing to do with the manager and I'd like to apologise for my reaction if anybody took any offence. It's not about me, it's about the boys and a great victory."

Gerrard, Liverpool's captain, accepted responsibility for the missed penalty that he would usually have taken, after Raheem Sterling went over Tim Howard's challenge. "I've scored a hat-trick against Everton and I wanted Daniel to experience that feeling," the midfielder said. "I'm sure the disappointment will see him strive to do better."

Rodgers drew a line under the brief spat by insisting the substitution was not in response to Sturridge's search for a hat-trick. "It wasn't a difficult decision to take him off," said the manager, who also confirmed he hopes to make a significant signing before the transfer window shuts on Friday. "His two finishes were sublime – he was a threat in the game and looks a threat every time he plays.

"We had to cut the risk by bringing him off. I felt the change balanced the team back up and there was no problem. I think he was a little frustrated after the penalty and he apologised to the group. If the manager decides to take you off it's not because you are playing poorly. Sometimes it's tactical but whatever reason it is you have to respect it and don't disrespect anyone. He hasn't done that [shown disrespect]. He was frustrated he missed the penalty. It was a brilliant performance from him."

The Sturridge spat could not take the gloss from an emphatic derby win and clinical performance by Liverpool. Rodgers said: "It was a brilliant team performance with brilliant defensive organisation, clinical in front of goal. Scored four and could have had more; a brilliant win for us. All wins are important but especially against your rivals. Psychologically it was a big win and one that gives confidence and belief to the squad. We just have to put the foot to the floor."

Rodgers would not say if victory in the 222nd Merseyside derby constituted his finest moment as Liverpool manager but it was unequivocally Roberto Martínez's worst since succeeding David Moyes at Everton. He recalled several players from injury only for their lack of fitness to be exposed and for Romelu Lukaku to join the injury list with suspected ankle ligament damage.

Martínez said: "We had a period of 13-14 minutes in the first half where we got ourselves in a position where we lost the game in a naive way. We were desperate to come here and be ourselves and give a performance to our fans they could be extremely happy and proud of. We played a bit too much with our heart at times. We started well enough. You could see how Liverpool wanted to hit us on the counter, which we should have used to our advantage.

"But we put ourselves in Liverpool's hands. We lost our concentration and our normal solid outlook. We just focused on trying to score goals and left ourselves way too open which is something we haven't done before this season."

Lukaku's injury could force Martínez back into the transfer market, he admitted, with the new signing Lacina Traoré his only established forward should the on-loan Chelsea striker face an extended spell on the sidelines. "The injuries caught up with us today," he said. "The players had to be rushed back and didn't have the match intensity you need and we looked a little bit out of sorts.

"We gave the ball away too cheaply and too easily and left ourselves exposed. We are a team that had the best defensive record in the division and lost only two games. From the first half you'd say that was not ourselves. It was a very uncharacteristic."

Merseyside police are investigating after saying "a number of coins and other small objects" were thrown on to the pitch in the first half. Suárez was targeted by Everton fans when taking a corner and handed a coin to the referee, Martin Atkinson.